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Colligative properties are properties of solutions that depend upon the ratio of the number of solute particles to the number of solvent molecules in a ... more
The Penman equation describes evaporation (E) from an open water surface, and was developed by Howard Penman in 1948. Penman’s equation requires ... more
Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by ... more
The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. It is named after its creator, O. Tetens who ... more
Concrete has relatively high compressive strength, but significantly lower tensile strength. As a result, without compensating, concrete would almost ... more
Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by ... more
Osmotic pressure is the pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane. The osmotic ... more
The Manning formula is also known as the Gauckler–Manning formula, or Gauckler–Manning–Strickler formula in Europe. In the United States, in practice, it ... more
The Froude number (Fr) is a dimensionless number defined as the ratio of a characteristic velocity to a gravitational wave velocity. It may equivalently be ... more
Strategy for (a)
To find the buoyant force, we must find the weight of water displaced. We can do this by using the densities of water and steel given in Table [insert table #] We note that, since the steel is completely submerged, its volume and the water’s volume are the same. Once we know the volume of water, we can find its mass and weight
First, we use the definition of density to find the steel’s volume, and then we substitute values for mass and density. This gives :
Because the steel is completely submerged, this is also the volume of water displaced, Vw. We can now find the mass of water displaced from the relationship between its volume and density, both of which are known. This gives:
By Archimedes’ principle, the weight of water displaced is m w g , so the buoyant force is:
The steel’s weight is 9.80×10 7 N , which is much greater than the buoyant force, so the steel will remain submerged.
Strategy for (b)
Here we are given the maximum volume of water the steel boat can displace. The buoyant force is the weight of this volume of water.
The mass of water displaced is found from its relationship to density and volume, both of which are known. That is:
The maximum buoyant force is the weight of this much water, or
Discussion
The maximum buoyant force is ten times the weight of the steel, meaning the ship can carry a load nine times its own weight without sinking.
Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/
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(a) Calculate the buoyant force on 10,000 metric tons (1.00×10 7 kg) of solid steel completely submerged in water, and compare this with the steel’s weight.
(b) What is the maximum buoyant force that water could exert on this same steel if it were shaped into a boat that could displace 1.00×10 5 m 3 of water?